A Monthly Time Series Model of Municipal Water Demand1

Abstract

In a recent article in the Water Resources Bulletin, Hansen and Narayanan (H-N) estimated several monthly time series models of municipal water demand for Salt Lake City, Utah. One model was then used to conduct an ex post analysis of water demand between 1975 and 1977 (Hansen and Narayanan, 1981. While H-N are to be commended for attempting to further knowledge in this area, several theoretical, econometric, and analysis problems exist in their study which we believe limits the usefulness of the material presented. MODEL FORMULATIONSeveral problems exist in the model formulation section. Problems are encountered from either misspecification of equations, careless editing or presentation, or inadequate development of a theoretical model. For example, D1 a nongrowing season dummy, is reported to have a value of zero during the growing season and one during the nongrowing season; but in the matrix and equation presentations, the reverse appears to be the case. In H-N's twin nongrowing season equations, D1 was omitted from the nongrowing season equation. Yet in the matrix presentation, the coefficient of D1 a p pears as (8; -$). Although 8: has not been identified, we assume it is the intercept of the growing season equation since both quantity demanded and the error term are asterisked. If this is the case, this implies that D1 has a value of one during the growing season and zero during the nongrowing months. Although this error may appear minor, it is unclear to us if H-N truly understand the equation and matrix manipulation they are attempting to explain. In addition, individuals with little knowledge of econometrics would find this section difficult to understand.The process H-N appear to use to estimate the appropriate demand model implies that little attention is paid to theoretical development. They appear to have estimated two OLS equations (H-N, Figure 2), eliminated nonsignificant variables, reestimated, then experimented with different seasonal variables.Using this ad hoc framework with the same data would tend to yield a model with significant explanatory variables and a high R2 value; however, what they have is a model developed to fit the data rather than determining if economic theory explains water demand.

Short‐term water consumption dynamics in El Paso, Texas

“…The earlier studies for the borderplex region focus primarily on annual data and do not examine the short-run time series characteristics of urban water demand. Development of monthly and quarterly frequency models should be feasible because they typically do not require extensive data sets [Hansen and Narayanan, 1981;Weber, 1989].…”

Challenges for creating a site-specific groundwater-use record for the Ozark Plateaus aquifer system (central USA) from 1900 to 2010

“…Researchers have explored long-term water quality (Cosby et al 1985;Hall and Smol 1996;Swank et al 2001;Burt et al 2014), but long-term water quantity research is generally limited to less than 15 years of record (Salas-La Cruz and Yevjevich 1972;Hansen and Narayanan 1981;Tsakiri and Zurbenko 2013;Yan et al 2016) and future water use is often projected using trend analysis (Brown 2000). Predictive modeling of recent water-use datasets (less than 20 years old) has helped to highlight explanatory variables that drive water use (Levin and Zarriello 2013; Committee on USGS Water Resources Research et al 2002), allowing water use to be estimated based on changing climate, population, or agriculture; however, techniques for modeling the temporal variation in water use may be limited in spatial scale.…”

An empirical analysis of Halifax municipal water consumption

“…Development of monthly short-term models is usually feasible because they typically do not require very extensive data sets (Hansen and Narayanan, 1981;Sankaran and Viraraghavan, 1992). Long-term, system of equation model development is often hindered by more voluminous data requirements.…”

“…In the case of the climate variables, the expected sign will vary. Increased rainfall will tend to reduce water usage, while higher temperatures will generally increase usage (Hansen and Narayanan, 1981;Fullerton and Elias, 2004).…”